Thank you for that information. If he is actively urinating and not just marking, then you want to start the potty training procedure again. When we get a rescue we never know their history which means we do not know if they were ever trained properly or if they were trained in such an old fashioned way that it has ruined them from training. Much is going to then depend on how the new owner handles retraining them as to how long it will take.
If the dog is marking then that is a completely different story and this is not something that can be trained out but only managed through vigilance, so it is very important to know the difference.
To start over the dog must not have run of the home because by allowing this you are setting him up to fail. He has gone his life with going inside the home so it is a learned behavior that we want him to unlearn. So it is important he be kept in a crate or on a tether next to his bed and food bowls as dog do not like to eliminate where they eat and sleep. If you can’t watch him 100% he must be contained and sometimes when people get busy around the house they actually tether the dog to them so they can watch them
Clean all areas you know that he has gone with a cleanser made just for dog urine or he will be attracted back to those spots.
Take him out via a leash and give a potty command, such as “go potty” and continue to say go potty even as he is eliminating so he associates the command with the act. Once he is done praise and reward but the reward must be special and something he will only get when he potties outside so he associates this with that command and the act. Something like hot dog slivers work well or cheese chunks.
Inside the home once you have cleaned all areas he is known to go in, start to sprinkle some of his kibble or treats in those areas so he begins to see them as an eating area. Eventually you can replace that with small bowls of water until he is trained